// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_PACKET_MATH_SSE_H
#define EIGEN_PACKET_MATH_SSE_H

namespace Eigen {

namespace internal {

#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8
#endif

#if !defined(EIGEN_VECTORIZE_AVX) && !defined(EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS)
// 32 bits =>  8 registers
// 64 bits => 16 registers
#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS (2 * sizeof(void*))
#endif

#ifdef EIGEN_VECTORIZE_FMA
#ifndef EIGEN_HAS_SINGLE_INSTRUCTION_MADD
#define EIGEN_HAS_SINGLE_INSTRUCTION_MADD
#endif
#endif

#if ((defined EIGEN_VECTORIZE_AVX) && (EIGEN_COMP_GNUC_STRICT || EIGEN_COMP_MINGW) && (__GXX_ABI_VERSION < 1004)) || EIGEN_OS_QNX
    // With GCC's default ABI version, a __m128 or __m256 are the same types and therefore we cannot
    // have overloads for both types without linking error.
    // One solution is to increase ABI version using -fabi-version=4 (or greater).
    // Otherwise, we workaround this inconvenience by wrapping 128bit types into the following helper
    // structure:
    typedef eigen_packet_wrapper<__m128> Packet4f;
    typedef eigen_packet_wrapper<__m128d> Packet2d;
#else
    typedef __m128 Packet4f;
    typedef __m128d Packet2d;
#endif

    typedef eigen_packet_wrapper<__m128i, 0> Packet4i;
    typedef eigen_packet_wrapper<__m128i, 1> Packet16b;

    template <> struct is_arithmetic<__m128>
    {
        enum
        {
            value = true
        };
    };
    template <> struct is_arithmetic<__m128i>
    {
        enum
        {
            value = true
        };
    };
    template <> struct is_arithmetic<__m128d>
    {
        enum
        {
            value = true
        };
    };
    template <> struct is_arithmetic<Packet4i>
    {
        enum
        {
            value = true
        };
    };
    template <> struct is_arithmetic<Packet16b>
    {
        enum
        {
            value = true
        };
    };

    template <int p, int q, int r, int s> struct shuffle_mask
    {
        enum
        {
            mask = (s) << 6 | (r) << 4 | (q) << 2 | (p)
        };
    };

// TODO: change the implementation of all swizzle* ops from macro to template,
#define vec4f_swizzle1(v, p, q, r, s) Packet4f(_mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(v), (shuffle_mask<p, q, r, s>::mask))))

#define vec4i_swizzle1(v, p, q, r, s) Packet4i(_mm_shuffle_epi32(v, (shuffle_mask<p, q, r, s>::mask)))

#define vec2d_swizzle1(v, p, q) Packet2d(_mm_castsi128_pd(_mm_shuffle_epi32(_mm_castpd_si128(v), (shuffle_mask<2 * p, 2 * p + 1, 2 * q, 2 * q + 1>::mask))))

#define vec4f_swizzle2(a, b, p, q, r, s) Packet4f(_mm_shuffle_ps((a), (b), (shuffle_mask<p, q, r, s>::mask)))

#define vec4i_swizzle2(a, b, p, q, r, s) \
    Packet4i(_mm_castps_si128((_mm_shuffle_ps(_mm_castsi128_ps(a), _mm_castsi128_ps(b), (shuffle_mask<p, q, r, s>::mask)))))

    EIGEN_STRONG_INLINE Packet4f vec4f_movelh(const Packet4f& a, const Packet4f& b) { return Packet4f(_mm_movelh_ps(a, b)); }
    EIGEN_STRONG_INLINE Packet4f vec4f_movehl(const Packet4f& a, const Packet4f& b) { return Packet4f(_mm_movehl_ps(a, b)); }
    EIGEN_STRONG_INLINE Packet4f vec4f_unpacklo(const Packet4f& a, const Packet4f& b) { return Packet4f(_mm_unpacklo_ps(a, b)); }
    EIGEN_STRONG_INLINE Packet4f vec4f_unpackhi(const Packet4f& a, const Packet4f& b) { return Packet4f(_mm_unpackhi_ps(a, b)); }
#define vec4f_duplane(a, p) vec4f_swizzle2(a, a, p, p, p, p)

#define vec2d_swizzle2(a, b, mask) Packet2d(_mm_shuffle_pd(a, b, mask))

    EIGEN_STRONG_INLINE Packet2d vec2d_unpacklo(const Packet2d& a, const Packet2d& b) { return Packet2d(_mm_unpacklo_pd(a, b)); }
    EIGEN_STRONG_INLINE Packet2d vec2d_unpackhi(const Packet2d& a, const Packet2d& b) { return Packet2d(_mm_unpackhi_pd(a, b)); }
#define vec2d_duplane(a, p) vec2d_swizzle2(a, a, (p << 1) | p)

#define _EIGEN_DECLARE_CONST_Packet4f(NAME, X) const Packet4f p4f_##NAME = pset1<Packet4f>(X)

#define _EIGEN_DECLARE_CONST_Packet2d(NAME, X) const Packet2d p2d_##NAME = pset1<Packet2d>(X)

#define _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(NAME, X) const Packet4f p4f_##NAME = pset1frombits<Packet4f>(X)

#define _EIGEN_DECLARE_CONST_Packet4i(NAME, X) const Packet4i p4i_##NAME = pset1<Packet4i>(X)

// Use the packet_traits defined in AVX/PacketMath.h instead if we're going
// to leverage AVX instructions.
#ifndef EIGEN_VECTORIZE_AVX
    template <> struct packet_traits<float> : default_packet_traits
    {
        typedef Packet4f type;
        typedef Packet4f half;
        enum
        {
            Vectorizable = 1,
            AlignedOnScalar = 1,
            size = 4,
            HasHalfPacket = 0,

            HasCmp = 1,
            HasDiv = 1,
            HasSin = EIGEN_FAST_MATH,
            HasCos = EIGEN_FAST_MATH,
            HasLog = 1,
            HasLog1p = 1,
            HasExpm1 = 1,
            HasNdtri = 1,
            HasExp = 1,
            HasBessel = 1,
            HasSqrt = 1,
            HasRsqrt = 1,
            HasTanh = EIGEN_FAST_MATH,
            HasErf = EIGEN_FAST_MATH,
            HasBlend = 1,
            HasCeil = 1,
            HasFloor = 1,
#ifdef EIGEN_VECTORIZE_SSE4_1
            HasRound = 1,
#endif
            HasRint = 1
        };
    };
    template <> struct packet_traits<double> : default_packet_traits
    {
        typedef Packet2d type;
        typedef Packet2d half;
        enum
        {
            Vectorizable = 1,
            AlignedOnScalar = 1,
            size = 2,
            HasHalfPacket = 0,

            HasCmp = 1,
            HasDiv = 1,
            HasLog = 1,
            HasExp = 1,
            HasSqrt = 1,
            HasRsqrt = 1,
            HasBlend = 1,
            HasFloor = 1,
            HasCeil = 1,
#ifdef EIGEN_VECTORIZE_SSE4_1
            HasRound = 1,
#endif
            HasRint = 1
        };
    };
#endif
    template <> struct packet_traits<int> : default_packet_traits
    {
        typedef Packet4i type;
        typedef Packet4i half;
        enum
        {
            Vectorizable = 1,
            AlignedOnScalar = 1,
            size = 4,

            HasShift = 1,
            HasBlend = 1
        };
    };

    template <> struct packet_traits<bool> : default_packet_traits
    {
        typedef Packet16b type;
        typedef Packet16b half;
        enum
        {
            Vectorizable = 1,
            AlignedOnScalar = 1,
            HasHalfPacket = 0,
            size = 16,

            HasAdd = 1,
            HasSub = 1,
            HasShift = 0,
            HasMul = 1,
            HasNegate = 1,
            HasAbs = 0,
            HasAbs2 = 0,
            HasMin = 0,
            HasMax = 0,
            HasConj = 0,
            HasSqrt = 1
        };
    };

    template <> struct unpacket_traits<Packet4f>
    {
        typedef float type;
        typedef Packet4f half;
        typedef Packet4i integer_packet;
        enum
        {
            size = 4,
            alignment = Aligned16,
            vectorizable = true,
            masked_load_available = false,
            masked_store_available = false
        };
    };
    template <> struct unpacket_traits<Packet2d>
    {
        typedef double type;
        typedef Packet2d half;
        enum
        {
            size = 2,
            alignment = Aligned16,
            vectorizable = true,
            masked_load_available = false,
            masked_store_available = false
        };
    };
    template <> struct unpacket_traits<Packet4i>
    {
        typedef int type;
        typedef Packet4i half;
        enum
        {
            size = 4,
            alignment = Aligned16,
            vectorizable = false,
            masked_load_available = false,
            masked_store_available = false
        };
    };
    template <> struct unpacket_traits<Packet16b>
    {
        typedef bool type;
        typedef Packet16b half;
        enum
        {
            size = 16,
            alignment = Aligned16,
            vectorizable = true,
            masked_load_available = false,
            masked_store_available = false
        };
    };

#ifndef EIGEN_VECTORIZE_AVX
    template <> struct scalar_div_cost<float, true>
    {
        enum
        {
            value = 7
        };
    };
    template <> struct scalar_div_cost<double, true>
    {
        enum
        {
            value = 8
        };
    };
#endif

#if EIGEN_COMP_MSVC == 1500
    // Workaround MSVC 9 internal compiler error.
    // TODO: It has been detected with win64 builds (amd64), so let's check whether it also happens in 32bits+SSE mode
    // TODO: let's check whether there does not exist a better fix, like adding a pset0() function. (it crashed on pset1(0)).
    template <> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float& from) { return _mm_set_ps(from, from, from, from); }
    template <> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double& from) { return _mm_set_pd(from, from); }
    template <> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int& from) { return _mm_set_epi32(from, from, from, from); }
#else
    template <> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float& from) { return _mm_set_ps1(from); }
    template <> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double& from) { return _mm_set1_pd(from); }
    template <> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int& from) { return _mm_set1_epi32(from); }
#endif
    template <> EIGEN_STRONG_INLINE Packet16b pset1<Packet16b>(const bool& from) { return _mm_set1_epi8(static_cast<char>(from)); }

    template <> EIGEN_STRONG_INLINE Packet4f pset1frombits<Packet4f>(unsigned int from) { return _mm_castsi128_ps(pset1<Packet4i>(from)); }
    template <> EIGEN_STRONG_INLINE Packet2d pset1frombits<Packet2d>(uint64_t from) { return _mm_castsi128_pd(_mm_set1_epi64x(from)); }

    template <> EIGEN_STRONG_INLINE Packet4f peven_mask(const Packet4f& /*a*/) { return _mm_castsi128_ps(_mm_set_epi32(0, -1, 0, -1)); }
    template <> EIGEN_STRONG_INLINE Packet4i peven_mask(const Packet4i& /*a*/) { return _mm_set_epi32(0, -1, 0, -1); }
    template <> EIGEN_STRONG_INLINE Packet2d peven_mask(const Packet2d& /*a*/) { return _mm_castsi128_pd(_mm_set_epi32(0, 0, -1, -1)); }

    template <> EIGEN_STRONG_INLINE Packet4f pzero(const Packet4f& /*a*/) { return _mm_setzero_ps(); }
    template <> EIGEN_STRONG_INLINE Packet2d pzero(const Packet2d& /*a*/) { return _mm_setzero_pd(); }
    template <> EIGEN_STRONG_INLINE Packet4i pzero(const Packet4i& /*a*/) { return _mm_setzero_si128(); }

// GCC generates a shufps instruction for _mm_set1_ps/_mm_load1_ps instead of the more efficient pshufd instruction.
// However, using inrinsics for pset1 makes gcc to generate crappy code in some cases (see bug 203)
// Using inline assembly is also not an option because then gcc fails to reorder properly the instructions.
// Therefore, we introduced the pload1 functions to be used in product kernels for which bug 203 does not apply.
// Also note that with AVX, we want it to generate a vbroadcastss.
#if EIGEN_COMP_GNUC_STRICT && (!defined __AVX__)
    template <> EIGEN_STRONG_INLINE Packet4f pload1<Packet4f>(const float* from) { return vec4f_swizzle1(_mm_load_ss(from), 0, 0, 0, 0); }
#endif

    template <> EIGEN_STRONG_INLINE Packet4f plset<Packet4f>(const float& a) { return _mm_add_ps(pset1<Packet4f>(a), _mm_set_ps(3, 2, 1, 0)); }
    template <> EIGEN_STRONG_INLINE Packet2d plset<Packet2d>(const double& a) { return _mm_add_pd(pset1<Packet2d>(a), _mm_set_pd(1, 0)); }
    template <> EIGEN_STRONG_INLINE Packet4i plset<Packet4i>(const int& a) { return _mm_add_epi32(pset1<Packet4i>(a), _mm_set_epi32(3, 2, 1, 0)); }

    template <> EIGEN_STRONG_INLINE Packet4f padd<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_add_ps(a, b); }
    template <> EIGEN_STRONG_INLINE Packet2d padd<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_add_pd(a, b); }
    template <> EIGEN_STRONG_INLINE Packet4i padd<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_add_epi32(a, b); }

    template <> EIGEN_STRONG_INLINE Packet16b padd<Packet16b>(const Packet16b& a, const Packet16b& b) { return _mm_or_si128(a, b); }

    template <> EIGEN_STRONG_INLINE Packet4f psub<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_sub_ps(a, b); }
    template <> EIGEN_STRONG_INLINE Packet2d psub<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_sub_pd(a, b); }
    template <> EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_sub_epi32(a, b); }
    template <> EIGEN_STRONG_INLINE Packet16b psub<Packet16b>(const Packet16b& a, const Packet16b& b) { return _mm_xor_si128(a, b); }

    template <> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b);
    template <> EIGEN_STRONG_INLINE Packet4f paddsub<Packet4f>(const Packet4f& a, const Packet4f& b)
    {
#ifdef EIGEN_VECTORIZE_SSE3
        return _mm_addsub_ps(a, b);
#else
        const Packet4f mask = _mm_castsi128_ps(_mm_setr_epi32(0x80000000, 0x0, 0x80000000, 0x0));
        return padd(a, pxor(mask, b));
#endif
    }

    template <> EIGEN_STRONG_INLINE Packet2d pxor<Packet2d>(const Packet2d&, const Packet2d&);
    template <> EIGEN_STRONG_INLINE Packet2d paddsub<Packet2d>(const Packet2d& a, const Packet2d& b)
    {
#ifdef EIGEN_VECTORIZE_SSE3
        return _mm_addsub_pd(a, b);
#else
        const Packet2d mask = _mm_castsi128_pd(_mm_setr_epi32(0x0, 0x80000000, 0x0, 0x0));
        return padd(a, pxor(mask, b));
#endif
    }

    template <> EIGEN_STRONG_INLINE Packet4f pnegate(const Packet4f& a)
    {
        const Packet4f mask = _mm_castsi128_ps(_mm_setr_epi32(0x80000000, 0x80000000, 0x80000000, 0x80000000));
        return _mm_xor_ps(a, mask);
    }
    template <> EIGEN_STRONG_INLINE Packet2d pnegate(const Packet2d& a)
    {
        const Packet2d mask = _mm_castsi128_pd(_mm_setr_epi32(0x0, 0x80000000, 0x0, 0x80000000));
        return _mm_xor_pd(a, mask);
    }
    template <> EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a) { return psub(Packet4i(_mm_setr_epi32(0, 0, 0, 0)), a); }

    template <> EIGEN_STRONG_INLINE Packet16b pnegate(const Packet16b& a) { return psub(pset1<Packet16b>(false), a); }

    template <> EIGEN_STRONG_INLINE Packet4f pconj(const Packet4f& a) { return a; }
    template <> EIGEN_STRONG_INLINE Packet2d pconj(const Packet2d& a) { return a; }
    template <> EIGEN_STRONG_INLINE Packet4i pconj(const Packet4i& a) { return a; }

    template <> EIGEN_STRONG_INLINE Packet4f pmul<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_mul_ps(a, b); }
    template <> EIGEN_STRONG_INLINE Packet2d pmul<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_mul_pd(a, b); }
    template <> EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b)
    {
#ifdef EIGEN_VECTORIZE_SSE4_1
        return _mm_mullo_epi32(a, b);
#else
        // this version is slightly faster than 4 scalar products
        return vec4i_swizzle1(
            vec4i_swizzle2(_mm_mul_epu32(a, b), _mm_mul_epu32(vec4i_swizzle1(a, 1, 0, 3, 2), vec4i_swizzle1(b, 1, 0, 3, 2)), 0, 2, 0, 2), 0, 2, 1, 3);
#endif
    }

    template <> EIGEN_STRONG_INLINE Packet16b pmul<Packet16b>(const Packet16b& a, const Packet16b& b) { return _mm_and_si128(a, b); }

    template <> EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_div_ps(a, b); }
    template <> EIGEN_STRONG_INLINE Packet2d pdiv<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_div_pd(a, b); }

    // for some weird raisons, it has to be overloaded for packet of integers
    template <> EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c) { return padd(pmul(a, b), c); }
#ifdef EIGEN_VECTORIZE_FMA
    template <> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return _mm_fmadd_ps(a, b, c); }
    template <> EIGEN_STRONG_INLINE Packet2d pmadd(const Packet2d& a, const Packet2d& b, const Packet2d& c) { return _mm_fmadd_pd(a, b, c); }
#endif

#ifdef EIGEN_VECTORIZE_SSE4_1
    template <> EIGEN_DEVICE_FUNC inline Packet4f pselect(const Packet4f& mask, const Packet4f& a, const Packet4f& b) { return _mm_blendv_ps(b, a, mask); }

    template <> EIGEN_DEVICE_FUNC inline Packet4i pselect(const Packet4i& mask, const Packet4i& a, const Packet4i& b)
    {
        return _mm_castps_si128(_mm_blendv_ps(_mm_castsi128_ps(b), _mm_castsi128_ps(a), _mm_castsi128_ps(mask)));
    }

    template <> EIGEN_DEVICE_FUNC inline Packet2d pselect(const Packet2d& mask, const Packet2d& a, const Packet2d& b) { return _mm_blendv_pd(b, a, mask); }

    template <> EIGEN_DEVICE_FUNC inline Packet16b pselect(const Packet16b& mask, const Packet16b& a, const Packet16b& b)
    {
        return _mm_blendv_epi8(b, a, mask);
    }
#else
    template <> EIGEN_DEVICE_FUNC inline Packet16b pselect(const Packet16b& mask, const Packet16b& a, const Packet16b& b)
    {
        Packet16b a_part = _mm_and_si128(mask, a);
        Packet16b b_part = _mm_andnot_si128(mask, b);
        return _mm_or_si128(a_part, b_part);
    }
#endif

    template <> EIGEN_STRONG_INLINE Packet4i ptrue<Packet4i>(const Packet4i& a) { return _mm_cmpeq_epi32(a, a); }
    template <> EIGEN_STRONG_INLINE Packet16b ptrue<Packet16b>(const Packet16b& a) { return _mm_cmpeq_epi8(a, a); }
    template <> EIGEN_STRONG_INLINE Packet4f ptrue<Packet4f>(const Packet4f& a)
    {
        Packet4i b = _mm_castps_si128(a);
        return _mm_castsi128_ps(_mm_cmpeq_epi32(b, b));
    }
    template <> EIGEN_STRONG_INLINE Packet2d ptrue<Packet2d>(const Packet2d& a)
    {
        Packet4i b = _mm_castpd_si128(a);
        return _mm_castsi128_pd(_mm_cmpeq_epi32(b, b));
    }

    template <> EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_and_ps(a, b); }
    template <> EIGEN_STRONG_INLINE Packet2d pand<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_and_pd(a, b); }
    template <> EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_and_si128(a, b); }
    template <> EIGEN_STRONG_INLINE Packet16b pand<Packet16b>(const Packet16b& a, const Packet16b& b) { return _mm_and_si128(a, b); }

    template <> EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_or_ps(a, b); }
    template <> EIGEN_STRONG_INLINE Packet2d por<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_or_pd(a, b); }
    template <> EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_or_si128(a, b); }
    template <> EIGEN_STRONG_INLINE Packet16b por<Packet16b>(const Packet16b& a, const Packet16b& b) { return _mm_or_si128(a, b); }

    template <> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_xor_ps(a, b); }
    template <> EIGEN_STRONG_INLINE Packet2d pxor<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_xor_pd(a, b); }
    template <> EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_xor_si128(a, b); }
    template <> EIGEN_STRONG_INLINE Packet16b pxor<Packet16b>(const Packet16b& a, const Packet16b& b) { return _mm_xor_si128(a, b); }

    template <> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_andnot_ps(b, a); }
    template <> EIGEN_STRONG_INLINE Packet2d pandnot<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_andnot_pd(b, a); }
    template <> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_andnot_si128(b, a); }

    template <> EIGEN_STRONG_INLINE Packet4f pcmp_le(const Packet4f& a, const Packet4f& b) { return _mm_cmple_ps(a, b); }
    template <> EIGEN_STRONG_INLINE Packet4f pcmp_lt(const Packet4f& a, const Packet4f& b) { return _mm_cmplt_ps(a, b); }
    template <> EIGEN_STRONG_INLINE Packet4f pcmp_lt_or_nan(const Packet4f& a, const Packet4f& b) { return _mm_cmpnge_ps(a, b); }
    template <> EIGEN_STRONG_INLINE Packet4f pcmp_eq(const Packet4f& a, const Packet4f& b) { return _mm_cmpeq_ps(a, b); }

    template <> EIGEN_STRONG_INLINE Packet2d pcmp_le(const Packet2d& a, const Packet2d& b) { return _mm_cmple_pd(a, b); }
    template <> EIGEN_STRONG_INLINE Packet2d pcmp_lt(const Packet2d& a, const Packet2d& b) { return _mm_cmplt_pd(a, b); }
    template <> EIGEN_STRONG_INLINE Packet2d pcmp_lt_or_nan(const Packet2d& a, const Packet2d& b) { return _mm_cmpnge_pd(a, b); }
    template <> EIGEN_STRONG_INLINE Packet2d pcmp_eq(const Packet2d& a, const Packet2d& b) { return _mm_cmpeq_pd(a, b); }

    template <> EIGEN_STRONG_INLINE Packet4i pcmp_lt(const Packet4i& a, const Packet4i& b) { return _mm_cmplt_epi32(a, b); }
    template <> EIGEN_STRONG_INLINE Packet4i pcmp_eq(const Packet4i& a, const Packet4i& b) { return _mm_cmpeq_epi32(a, b); }
    template <> EIGEN_STRONG_INLINE Packet16b pcmp_eq(const Packet16b& a, const Packet16b& b) { return _mm_cmpeq_epi8(a, b); }
    template <> EIGEN_STRONG_INLINE Packet4i pcmp_le(const Packet4i& a, const Packet4i& b) { return por(pcmp_lt(a, b), pcmp_eq(a, b)); }

    template <> EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const Packet4f& b)
    {
#if EIGEN_COMP_GNUC && EIGEN_COMP_GNUC < 63
// There appears to be a bug in GCC, by which the optimizer may
// flip the argument order in calls to _mm_min_ps, so we have to
// resort to inline ASM here. This is supposed to be fixed in gcc6.3,
// see also: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=72867
#ifdef EIGEN_VECTORIZE_AVX
        Packet4f res;
        asm("vminps %[a], %[b], %[res]" : [res] "=x"(res) : [a] "x"(a), [b] "x"(b));
#else
        Packet4f res = b;
        asm("minps %[a], %[res]" : [res] "+x"(res) : [a] "x"(a));
#endif
        return res;
#else
        // Arguments are reversed to match NaN propagation behavior of std::min.
        return _mm_min_ps(b, a);
#endif
    }
    template <> EIGEN_STRONG_INLINE Packet2d pmin<Packet2d>(const Packet2d& a, const Packet2d& b)
    {
#if EIGEN_COMP_GNUC && EIGEN_COMP_GNUC < 63
// There appears to be a bug in GCC, by which the optimizer may
// flip the argument order in calls to _mm_min_pd, so we have to
// resort to inline ASM here. This is supposed to be fixed in gcc6.3,
// see also: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=72867
#ifdef EIGEN_VECTORIZE_AVX
        Packet2d res;
        asm("vminpd %[a], %[b], %[res]" : [res] "=x"(res) : [a] "x"(a), [b] "x"(b));
#else
        Packet2d res = b;
        asm("minpd %[a], %[res]" : [res] "+x"(res) : [a] "x"(a));
#endif
        return res;
#else
        // Arguments are reversed to match NaN propagation behavior of std::min.
        return _mm_min_pd(b, a);
#endif
    }
    template <> EIGEN_STRONG_INLINE Packet4i pmin<Packet4i>(const Packet4i& a, const Packet4i& b)
    {
#ifdef EIGEN_VECTORIZE_SSE4_1
        return _mm_min_epi32(a, b);
#else
        // after some bench, this version *is* faster than a scalar implementation
        Packet4i mask = _mm_cmplt_epi32(a, b);
        return _mm_or_si128(_mm_and_si128(mask, a), _mm_andnot_si128(mask, b));
#endif
    }

    template <> EIGEN_STRONG_INLINE Packet4f pmax<Packet4f>(const Packet4f& a, const Packet4f& b)
    {
#if EIGEN_COMP_GNUC && EIGEN_COMP_GNUC < 63
// There appears to be a bug in GCC, by which the optimizer may
// flip the argument order in calls to _mm_max_ps, so we have to
// resort to inline ASM here. This is supposed to be fixed in gcc6.3,
// see also: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=72867
#ifdef EIGEN_VECTORIZE_AVX
        Packet4f res;
        asm("vmaxps %[a], %[b], %[res]" : [res] "=x"(res) : [a] "x"(a), [b] "x"(b));
#else
        Packet4f res = b;
        asm("maxps %[a], %[res]" : [res] "+x"(res) : [a] "x"(a));
#endif
        return res;
#else
        // Arguments are reversed to match NaN propagation behavior of std::max.
        return _mm_max_ps(b, a);
#endif
    }
    template <> EIGEN_STRONG_INLINE Packet2d pmax<Packet2d>(const Packet2d& a, const Packet2d& b)
    {
#if EIGEN_COMP_GNUC && EIGEN_COMP_GNUC < 63
// There appears to be a bug in GCC, by which the optimizer may
// flip the argument order in calls to _mm_max_pd, so we have to
// resort to inline ASM here. This is supposed to be fixed in gcc6.3,
// see also: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=72867
#ifdef EIGEN_VECTORIZE_AVX
        Packet2d res;
        asm("vmaxpd %[a], %[b], %[res]" : [res] "=x"(res) : [a] "x"(a), [b] "x"(b));
#else
        Packet2d res = b;
        asm("maxpd %[a], %[res]" : [res] "+x"(res) : [a] "x"(a));
#endif
        return res;
#else
        // Arguments are reversed to match NaN propagation behavior of std::max.
        return _mm_max_pd(b, a);
#endif
    }
    template <> EIGEN_STRONG_INLINE Packet4i pmax<Packet4i>(const Packet4i& a, const Packet4i& b)
    {
#ifdef EIGEN_VECTORIZE_SSE4_1
        return _mm_max_epi32(a, b);
#else
        // after some bench, this version *is* faster than a scalar implementation
        Packet4i mask = _mm_cmpgt_epi32(a, b);
        return _mm_or_si128(_mm_and_si128(mask, a), _mm_andnot_si128(mask, b));
#endif
    }

    template <typename Packet, typename Op> EIGEN_STRONG_INLINE Packet pminmax_propagate_numbers(const Packet& a, const Packet& b, Op op)
    {
        // In this implementation, we take advantage of the fact that pmin/pmax for SSE
        // always return a if either a or b is NaN.
        Packet not_nan_mask_a = pcmp_eq(a, a);
        Packet m = op(a, b);
        return pselect<Packet>(not_nan_mask_a, m, b);
    }

    template <typename Packet, typename Op> EIGEN_STRONG_INLINE Packet pminmax_propagate_nan(const Packet& a, const Packet& b, Op op)
    {
        // In this implementation, we take advantage of the fact that pmin/pmax for SSE
        // always return a if either a or b is NaN.
        Packet not_nan_mask_a = pcmp_eq(a, a);
        Packet m = op(b, a);
        return pselect<Packet>(not_nan_mask_a, m, a);
    }

    // Add specializations for min/max with prescribed NaN progation.
    template <> EIGEN_STRONG_INLINE Packet4f pmin<PropagateNumbers, Packet4f>(const Packet4f& a, const Packet4f& b)
    {
        return pminmax_propagate_numbers(a, b, pmin<Packet4f>);
    }
    template <> EIGEN_STRONG_INLINE Packet2d pmin<PropagateNumbers, Packet2d>(const Packet2d& a, const Packet2d& b)
    {
        return pminmax_propagate_numbers(a, b, pmin<Packet2d>);
    }
    template <> EIGEN_STRONG_INLINE Packet4f pmax<PropagateNumbers, Packet4f>(const Packet4f& a, const Packet4f& b)
    {
        return pminmax_propagate_numbers(a, b, pmax<Packet4f>);
    }
    template <> EIGEN_STRONG_INLINE Packet2d pmax<PropagateNumbers, Packet2d>(const Packet2d& a, const Packet2d& b)
    {
        return pminmax_propagate_numbers(a, b, pmax<Packet2d>);
    }
    template <> EIGEN_STRONG_INLINE Packet4f pmin<PropagateNaN, Packet4f>(const Packet4f& a, const Packet4f& b)
    {
        return pminmax_propagate_nan(a, b, pmin<Packet4f>);
    }
    template <> EIGEN_STRONG_INLINE Packet2d pmin<PropagateNaN, Packet2d>(const Packet2d& a, const Packet2d& b)
    {
        return pminmax_propagate_nan(a, b, pmin<Packet2d>);
    }
    template <> EIGEN_STRONG_INLINE Packet4f pmax<PropagateNaN, Packet4f>(const Packet4f& a, const Packet4f& b)
    {
        return pminmax_propagate_nan(a, b, pmax<Packet4f>);
    }
    template <> EIGEN_STRONG_INLINE Packet2d pmax<PropagateNaN, Packet2d>(const Packet2d& a, const Packet2d& b)
    {
        return pminmax_propagate_nan(a, b, pmax<Packet2d>);
    }

    template <int N> EIGEN_STRONG_INLINE Packet4i parithmetic_shift_right(const Packet4i& a) { return _mm_srai_epi32(a, N); }
    template <int N> EIGEN_STRONG_INLINE Packet4i plogical_shift_right(const Packet4i& a) { return _mm_srli_epi32(a, N); }
    template <int N> EIGEN_STRONG_INLINE Packet4i plogical_shift_left(const Packet4i& a) { return _mm_slli_epi32(a, N); }

    template <> EIGEN_STRONG_INLINE Packet4f pabs(const Packet4f& a)
    {
        const Packet4f mask = _mm_castsi128_ps(_mm_setr_epi32(0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF));
        return _mm_and_ps(a, mask);
    }
    template <> EIGEN_STRONG_INLINE Packet2d pabs(const Packet2d& a)
    {
        const Packet2d mask = _mm_castsi128_pd(_mm_setr_epi32(0xFFFFFFFF, 0x7FFFFFFF, 0xFFFFFFFF, 0x7FFFFFFF));
        return _mm_and_pd(a, mask);
    }
    template <> EIGEN_STRONG_INLINE Packet4i pabs(const Packet4i& a)
    {
#ifdef EIGEN_VECTORIZE_SSSE3
        return _mm_abs_epi32(a);
#else
        Packet4i aux = _mm_srai_epi32(a, 31);
        return _mm_sub_epi32(_mm_xor_si128(a, aux), aux);
#endif
    }

#ifdef EIGEN_VECTORIZE_SSE4_1
    template <> EIGEN_STRONG_INLINE Packet4f pround<Packet4f>(const Packet4f& a)
    {
        // Unfortunatly _mm_round_ps doesn't have a rounding mode to implement numext::round.
        const Packet4f mask = pset1frombits<Packet4f>(0x80000000u);
        const Packet4f prev0dot5 = pset1frombits<Packet4f>(0x3EFFFFFFu);
        return _mm_round_ps(padd(por(pand(a, mask), prev0dot5), a), _MM_FROUND_TO_ZERO);
    }

    template <> EIGEN_STRONG_INLINE Packet2d pround<Packet2d>(const Packet2d& a)
    {
        const Packet2d mask = _mm_castsi128_pd(_mm_set_epi64x(0x8000000000000000ull, 0x8000000000000000ull));
        const Packet2d prev0dot5 = _mm_castsi128_pd(_mm_set_epi64x(0x3FDFFFFFFFFFFFFFull, 0x3FDFFFFFFFFFFFFFull));
        return _mm_round_pd(padd(por(pand(a, mask), prev0dot5), a), _MM_FROUND_TO_ZERO);
    }

    template <> EIGEN_STRONG_INLINE Packet4f print<Packet4f>(const Packet4f& a) { return _mm_round_ps(a, _MM_FROUND_CUR_DIRECTION); }
    template <> EIGEN_STRONG_INLINE Packet2d print<Packet2d>(const Packet2d& a) { return _mm_round_pd(a, _MM_FROUND_CUR_DIRECTION); }

    template <> EIGEN_STRONG_INLINE Packet4f pceil<Packet4f>(const Packet4f& a) { return _mm_ceil_ps(a); }
    template <> EIGEN_STRONG_INLINE Packet2d pceil<Packet2d>(const Packet2d& a) { return _mm_ceil_pd(a); }

    template <> EIGEN_STRONG_INLINE Packet4f pfloor<Packet4f>(const Packet4f& a) { return _mm_floor_ps(a); }
    template <> EIGEN_STRONG_INLINE Packet2d pfloor<Packet2d>(const Packet2d& a) { return _mm_floor_pd(a); }
#else
    template <> EIGEN_STRONG_INLINE Packet4f print(const Packet4f& a)
    {
        // Adds and subtracts signum(a) * 2^23 to force rounding.
        const Packet4f limit = pset1<Packet4f>(static_cast<float>(1 << 23));
        const Packet4f abs_a = pabs(a);
        Packet4f r = padd(abs_a, limit);
        // Don't compile-away addition and subtraction.
        EIGEN_OPTIMIZATION_BARRIER(r);
        r = psub(r, limit);
        // If greater than limit, simply return a.  Otherwise, account for sign.
        r = pselect(pcmp_lt(abs_a, limit), pselect(pcmp_lt(a, pzero(a)), pnegate(r), r), a);
        return r;
    }

    template <> EIGEN_STRONG_INLINE Packet2d print(const Packet2d& a)
    {
        // Adds and subtracts signum(a) * 2^52 to force rounding.
        const Packet2d limit = pset1<Packet2d>(static_cast<double>(1ull << 52));
        const Packet2d abs_a = pabs(a);
        Packet2d r = padd(abs_a, limit);
        // Don't compile-away addition and subtraction.
        EIGEN_OPTIMIZATION_BARRIER(r);
        r = psub(r, limit);
        // If greater than limit, simply return a.  Otherwise, account for sign.
        r = pselect(pcmp_lt(abs_a, limit), pselect(pcmp_lt(a, pzero(a)), pnegate(r), r), a);
        return r;
    }

    template <> EIGEN_STRONG_INLINE Packet4f pfloor<Packet4f>(const Packet4f& a)
    {
        const Packet4f cst_1 = pset1<Packet4f>(1.0f);
        Packet4f tmp = print<Packet4f>(a);
        // If greater, subtract one.
        Packet4f mask = _mm_cmpgt_ps(tmp, a);
        mask = pand(mask, cst_1);
        return psub(tmp, mask);
    }

    template <> EIGEN_STRONG_INLINE Packet2d pfloor<Packet2d>(const Packet2d& a)
    {
        const Packet2d cst_1 = pset1<Packet2d>(1.0);
        Packet2d tmp = print<Packet2d>(a);
        // If greater, subtract one.
        Packet2d mask = _mm_cmpgt_pd(tmp, a);
        mask = pand(mask, cst_1);
        return psub(tmp, mask);
    }

    template <> EIGEN_STRONG_INLINE Packet4f pceil<Packet4f>(const Packet4f& a)
    {
        const Packet4f cst_1 = pset1<Packet4f>(1.0f);
        Packet4f tmp = print<Packet4f>(a);
        // If smaller, add one.
        Packet4f mask = _mm_cmplt_ps(tmp, a);
        mask = pand(mask, cst_1);
        return padd(tmp, mask);
    }

    template <> EIGEN_STRONG_INLINE Packet2d pceil<Packet2d>(const Packet2d& a)
    {
        const Packet2d cst_1 = pset1<Packet2d>(1.0);
        Packet2d tmp = print<Packet2d>(a);
        // If smaller, add one.
        Packet2d mask = _mm_cmplt_pd(tmp, a);
        mask = pand(mask, cst_1);
        return padd(tmp, mask);
    }
#endif

    template <> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float* from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm_load_ps(from); }
    template <> EIGEN_STRONG_INLINE Packet2d pload<Packet2d>(const double* from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm_load_pd(from); }
    template <> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int* from)
    {
        EIGEN_DEBUG_ALIGNED_LOAD return _mm_load_si128(reinterpret_cast<const __m128i*>(from));
    }
    template <> EIGEN_STRONG_INLINE Packet16b pload<Packet16b>(const bool* from)
    {
        EIGEN_DEBUG_ALIGNED_LOAD return _mm_load_si128(reinterpret_cast<const __m128i*>(from));
    }

#if EIGEN_COMP_MSVC
    template <> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from)
    {
        EIGEN_DEBUG_UNALIGNED_LOAD
#if (EIGEN_COMP_MSVC == 1600)
        // NOTE Some version of MSVC10 generates bad code when using _mm_loadu_ps
        // (i.e., it does not generate an unaligned load!!
        __m128 res = _mm_loadl_pi(_mm_set1_ps(0.0f), (const __m64*)(from));
        res = _mm_loadh_pi(res, (const __m64*)(from + 2));
        return res;
#else
        return _mm_loadu_ps(from);
#endif
    }
#else
    // NOTE: with the code below, MSVC's compiler crashes!

    template <> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from)
    {
        EIGEN_DEBUG_UNALIGNED_LOAD
        return _mm_loadu_ps(from);
    }
#endif

    template <> EIGEN_STRONG_INLINE Packet2d ploadu<Packet2d>(const double* from)
    {
        EIGEN_DEBUG_UNALIGNED_LOAD
        return _mm_loadu_pd(from);
    }
    template <> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from)
    {
        EIGEN_DEBUG_UNALIGNED_LOAD
        return _mm_loadu_si128(reinterpret_cast<const __m128i*>(from));
    }
    template <> EIGEN_STRONG_INLINE Packet16b ploadu<Packet16b>(const bool* from)
    {
        EIGEN_DEBUG_UNALIGNED_LOAD
        return _mm_loadu_si128(reinterpret_cast<const __m128i*>(from));
    }

    template <> EIGEN_STRONG_INLINE Packet4f ploaddup<Packet4f>(const float* from)
    {
        return vec4f_swizzle1(_mm_castpd_ps(_mm_load_sd(reinterpret_cast<const double*>(from))), 0, 0, 1, 1);
    }
    template <> EIGEN_STRONG_INLINE Packet2d ploaddup<Packet2d>(const double* from) { return pset1<Packet2d>(from[0]); }
    template <> EIGEN_STRONG_INLINE Packet4i ploaddup<Packet4i>(const int* from)
    {
        Packet4i tmp;
        tmp = _mm_loadl_epi64(reinterpret_cast<const __m128i*>(from));
        return vec4i_swizzle1(tmp, 0, 0, 1, 1);
    }

    // Loads 8 bools from memory and returns the packet
    // {b0, b0, b1, b1, b2, b2, b3, b3, b4, b4, b5, b5, b6, b6, b7, b7}
    template <> EIGEN_STRONG_INLINE Packet16b ploaddup<Packet16b>(const bool* from)
    {
        __m128i tmp = _mm_castpd_si128(pload1<Packet2d>(reinterpret_cast<const double*>(from)));
        return _mm_unpacklo_epi8(tmp, tmp);
    }

    // Loads 4 bools from memory and returns the packet
    // {b0, b0  b0, b0, b1, b1, b1, b1, b2, b2, b2, b2, b3, b3, b3, b3}
    template <> EIGEN_STRONG_INLINE Packet16b ploadquad<Packet16b>(const bool* from)
    {
        __m128i tmp = _mm_castps_si128(pload1<Packet4f>(reinterpret_cast<const float*>(from)));
        tmp = _mm_unpacklo_epi8(tmp, tmp);
        return _mm_unpacklo_epi16(tmp, tmp);
    }

    template <> EIGEN_STRONG_INLINE void pstore<float>(float* to, const Packet4f& from) { EIGEN_DEBUG_ALIGNED_STORE _mm_store_ps(to, from); }
    template <> EIGEN_STRONG_INLINE void pstore<double>(double* to, const Packet2d& from) { EIGEN_DEBUG_ALIGNED_STORE _mm_store_pd(to, from); }
    template <> EIGEN_STRONG_INLINE void pstore<int>(int* to, const Packet4i& from)
    {
        EIGEN_DEBUG_ALIGNED_STORE _mm_store_si128(reinterpret_cast<__m128i*>(to), from);
    }
    template <> EIGEN_STRONG_INLINE void pstore<bool>(bool* to, const Packet16b& from)
    {
        EIGEN_DEBUG_ALIGNED_STORE _mm_store_si128(reinterpret_cast<__m128i*>(to), from);
    }

    template <> EIGEN_STRONG_INLINE void pstoreu<double>(double* to, const Packet2d& from) { EIGEN_DEBUG_UNALIGNED_STORE _mm_storeu_pd(to, from); }
    template <> EIGEN_STRONG_INLINE void pstoreu<float>(float* to, const Packet4f& from) { EIGEN_DEBUG_UNALIGNED_STORE _mm_storeu_ps(to, from); }
    template <> EIGEN_STRONG_INLINE void pstoreu<int>(int* to, const Packet4i& from)
    {
        EIGEN_DEBUG_UNALIGNED_STORE _mm_storeu_si128(reinterpret_cast<__m128i*>(to), from);
    }
    template <> EIGEN_STRONG_INLINE void pstoreu<bool>(bool* to, const Packet16b& from)
    {
        EIGEN_DEBUG_ALIGNED_STORE _mm_storeu_si128(reinterpret_cast<__m128i*>(to), from);
    }

    template <> EIGEN_DEVICE_FUNC inline Packet4f pgather<float, Packet4f>(const float* from, Index stride)
    {
        return _mm_set_ps(from[3 * stride], from[2 * stride], from[1 * stride], from[0 * stride]);
    }
    template <> EIGEN_DEVICE_FUNC inline Packet2d pgather<double, Packet2d>(const double* from, Index stride)
    {
        return _mm_set_pd(from[1 * stride], from[0 * stride]);
    }
    template <> EIGEN_DEVICE_FUNC inline Packet4i pgather<int, Packet4i>(const int* from, Index stride)
    {
        return _mm_set_epi32(from[3 * stride], from[2 * stride], from[1 * stride], from[0 * stride]);
    }

    template <> EIGEN_DEVICE_FUNC inline Packet16b pgather<bool, Packet16b>(const bool* from, Index stride)
    {
        return _mm_set_epi8(from[15 * stride],
                            from[14 * stride],
                            from[13 * stride],
                            from[12 * stride],
                            from[11 * stride],
                            from[10 * stride],
                            from[9 * stride],
                            from[8 * stride],
                            from[7 * stride],
                            from[6 * stride],
                            from[5 * stride],
                            from[4 * stride],
                            from[3 * stride],
                            from[2 * stride],
                            from[1 * stride],
                            from[0 * stride]);
    }

    template <> EIGEN_DEVICE_FUNC inline void pscatter<float, Packet4f>(float* to, const Packet4f& from, Index stride)
    {
        to[stride * 0] = _mm_cvtss_f32(from);
        to[stride * 1] = _mm_cvtss_f32(_mm_shuffle_ps(from, from, 1));
        to[stride * 2] = _mm_cvtss_f32(_mm_shuffle_ps(from, from, 2));
        to[stride * 3] = _mm_cvtss_f32(_mm_shuffle_ps(from, from, 3));
    }
    template <> EIGEN_DEVICE_FUNC inline void pscatter<double, Packet2d>(double* to, const Packet2d& from, Index stride)
    {
        to[stride * 0] = _mm_cvtsd_f64(from);
        to[stride * 1] = _mm_cvtsd_f64(_mm_shuffle_pd(from, from, 1));
    }
    template <> EIGEN_DEVICE_FUNC inline void pscatter<int, Packet4i>(int* to, const Packet4i& from, Index stride)
    {
        to[stride * 0] = _mm_cvtsi128_si32(from);
        to[stride * 1] = _mm_cvtsi128_si32(_mm_shuffle_epi32(from, 1));
        to[stride * 2] = _mm_cvtsi128_si32(_mm_shuffle_epi32(from, 2));
        to[stride * 3] = _mm_cvtsi128_si32(_mm_shuffle_epi32(from, 3));
    }
    template <> EIGEN_DEVICE_FUNC inline void pscatter<bool, Packet16b>(bool* to, const Packet16b& from, Index stride)
    {
        to[4 * stride * 0] = _mm_cvtsi128_si32(from);
        to[4 * stride * 1] = _mm_cvtsi128_si32(_mm_shuffle_epi32(from, 1));
        to[4 * stride * 2] = _mm_cvtsi128_si32(_mm_shuffle_epi32(from, 2));
        to[4 * stride * 3] = _mm_cvtsi128_si32(_mm_shuffle_epi32(from, 3));
    }

    // some compilers might be tempted to perform multiple moves instead of using a vector path.
    template <> EIGEN_STRONG_INLINE void pstore1<Packet4f>(float* to, const float& a)
    {
        Packet4f pa = _mm_set_ss(a);
        pstore(to, Packet4f(vec4f_swizzle1(pa, 0, 0, 0, 0)));
    }
    // some compilers might be tempted to perform multiple moves instead of using a vector path.
    template <> EIGEN_STRONG_INLINE void pstore1<Packet2d>(double* to, const double& a)
    {
        Packet2d pa = _mm_set_sd(a);
        pstore(to, Packet2d(vec2d_swizzle1(pa, 0, 0)));
    }

#if EIGEN_COMP_PGI && EIGEN_COMP_PGI < 1900
    typedef const void* SsePrefetchPtrType;
#else
    typedef const char* SsePrefetchPtrType;
#endif

#ifndef EIGEN_VECTORIZE_AVX
    template <> EIGEN_STRONG_INLINE void prefetch<float>(const float* addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }
    template <> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }
    template <> EIGEN_STRONG_INLINE void prefetch<int>(const int* addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }
#endif

#if EIGEN_COMP_MSVC_STRICT && EIGEN_OS_WIN64
    // The temporary variable fixes an internal compilation error in vs <= 2008 and a wrong-result bug in vs 2010
    // Direct of the struct members fixed bug #62.
    template <> EIGEN_STRONG_INLINE float pfirst<Packet4f>(const Packet4f& a) { return a.m128_f32[0]; }
    template <> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) { return a.m128d_f64[0]; }
    template <> EIGEN_STRONG_INLINE int pfirst<Packet4i>(const Packet4i& a)
    {
        int x = _mm_cvtsi128_si32(a);
        return x;
    }
#elif EIGEN_COMP_MSVC_STRICT
    // The temporary variable fixes an internal compilation error in vs <= 2008 and a wrong-result bug in vs 2010
    template <> EIGEN_STRONG_INLINE float pfirst<Packet4f>(const Packet4f& a)
    {
        float x = _mm_cvtss_f32(a);
        return x;
    }
    template <> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a)
    {
        double x = _mm_cvtsd_f64(a);
        return x;
    }
    template <> EIGEN_STRONG_INLINE int pfirst<Packet4i>(const Packet4i& a)
    {
        int x = _mm_cvtsi128_si32(a);
        return x;
    }
#else
    template <> EIGEN_STRONG_INLINE float pfirst<Packet4f>(const Packet4f& a) { return _mm_cvtss_f32(a); }
    template <> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) { return _mm_cvtsd_f64(a); }
    template <> EIGEN_STRONG_INLINE int pfirst<Packet4i>(const Packet4i& a) { return _mm_cvtsi128_si32(a); }
#endif
    template <> EIGEN_STRONG_INLINE bool pfirst<Packet16b>(const Packet16b& a)
    {
        int x = _mm_cvtsi128_si32(a);
        return static_cast<bool>(x & 1);
    }

    template <> EIGEN_STRONG_INLINE Packet4f preverse(const Packet4f& a) { return _mm_shuffle_ps(a, a, 0x1B); }
    template <> EIGEN_STRONG_INLINE Packet2d preverse(const Packet2d& a) { return _mm_shuffle_pd(a, a, 0x1); }
    template <> EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a) { return _mm_shuffle_epi32(a, 0x1B); }
    template <> EIGEN_STRONG_INLINE Packet16b preverse(const Packet16b& a)
    {
#ifdef EIGEN_VECTORIZE_SSSE3
        __m128i mask = _mm_set_epi8(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15);
        return _mm_shuffle_epi8(a, mask);
#else
        Packet16b tmp = _mm_shuffle_epi32(a, _MM_SHUFFLE(0, 1, 2, 3));
        tmp = _mm_shufflehi_epi16(_mm_shufflelo_epi16(tmp, _MM_SHUFFLE(2, 3, 0, 1)), _MM_SHUFFLE(2, 3, 0, 1));
        return _mm_or_si128(_mm_slli_epi16(tmp, 8), _mm_srli_epi16(tmp, 8));
#endif
    }

    template <> EIGEN_STRONG_INLINE Packet4f pfrexp<Packet4f>(const Packet4f& a, Packet4f& exponent) { return pfrexp_generic(a, exponent); }

    // Extract exponent without existence of Packet2l.
    template <> EIGEN_STRONG_INLINE Packet2d pfrexp_generic_get_biased_exponent(const Packet2d& a)
    {
        const Packet2d cst_exp_mask = pset1frombits<Packet2d>(static_cast<uint64_t>(0x7ff0000000000000ull));
        __m128i a_expo = _mm_srli_epi64(_mm_castpd_si128(pand(a, cst_exp_mask)), 52);
        return _mm_cvtepi32_pd(vec4i_swizzle1(a_expo, 0, 2, 1, 3));
    }

    template <> EIGEN_STRONG_INLINE Packet2d pfrexp<Packet2d>(const Packet2d& a, Packet2d& exponent) { return pfrexp_generic(a, exponent); }

    template <> EIGEN_STRONG_INLINE Packet4f pldexp<Packet4f>(const Packet4f& a, const Packet4f& exponent) { return pldexp_generic(a, exponent); }

    // We specialize pldexp here, since the generic implementation uses Packet2l, which is not well
    // supported by SSE, and has more range than is needed for exponents.
    template <> EIGEN_STRONG_INLINE Packet2d pldexp<Packet2d>(const Packet2d& a, const Packet2d& exponent)
    {
        // Clamp exponent to [-2099, 2099]
        const Packet2d max_exponent = pset1<Packet2d>(2099.0);
        const Packet2d e = pmin(pmax(exponent, pnegate(max_exponent)), max_exponent);

        // Convert e to integer and swizzle to low-order bits.
        const Packet4i ei = vec4i_swizzle1(_mm_cvtpd_epi32(e), 0, 3, 1, 3);

        // Split 2^e into four factors and multiply:
        const Packet4i bias = _mm_set_epi32(0, 1023, 0, 1023);
        Packet4i b = parithmetic_shift_right<2>(ei);                       // floor(e/4)
        Packet2d c = _mm_castsi128_pd(_mm_slli_epi64(padd(b, bias), 52));  // 2^b
        Packet2d out = pmul(pmul(pmul(a, c), c), c);                       // a * 2^(3b)
        b = psub(psub(psub(ei, b), b), b);                                 // e - 3b
        c = _mm_castsi128_pd(_mm_slli_epi64(padd(b, bias), 52));           // 2^(e - 3b)
        out = pmul(out, c);                                                // a * 2^e
        return out;
    }

// with AVX, the default implementations based on pload1 are faster
#ifndef __AVX__
    template <> EIGEN_STRONG_INLINE void pbroadcast4<Packet4f>(const float* a, Packet4f& a0, Packet4f& a1, Packet4f& a2, Packet4f& a3)
    {
        a3 = pload<Packet4f>(a);
        a0 = vec4f_swizzle1(a3, 0, 0, 0, 0);
        a1 = vec4f_swizzle1(a3, 1, 1, 1, 1);
        a2 = vec4f_swizzle1(a3, 2, 2, 2, 2);
        a3 = vec4f_swizzle1(a3, 3, 3, 3, 3);
    }
    template <> EIGEN_STRONG_INLINE void pbroadcast4<Packet2d>(const double* a, Packet2d& a0, Packet2d& a1, Packet2d& a2, Packet2d& a3)
    {
#ifdef EIGEN_VECTORIZE_SSE3
        a0 = _mm_loaddup_pd(a + 0);
        a1 = _mm_loaddup_pd(a + 1);
        a2 = _mm_loaddup_pd(a + 2);
        a3 = _mm_loaddup_pd(a + 3);
#else
        a1 = pload<Packet2d>(a);
        a0 = vec2d_swizzle1(a1, 0, 0);
        a1 = vec2d_swizzle1(a1, 1, 1);
        a3 = pload<Packet2d>(a + 2);
        a2 = vec2d_swizzle1(a3, 0, 0);
        a3 = vec2d_swizzle1(a3, 1, 1);
#endif
    }
#endif

    EIGEN_STRONG_INLINE void punpackp(Packet4f* vecs)
    {
        vecs[1] = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(vecs[0]), 0x55));
        vecs[2] = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(vecs[0]), 0xAA));
        vecs[3] = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(vecs[0]), 0xFF));
        vecs[0] = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(vecs[0]), 0x00));
    }

    template <> EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a)
    {
        // Disable SSE3 _mm_hadd_pd that is extremely slow on all existing Intel's architectures
        // (from Nehalem to Haswell)
        // #ifdef EIGEN_VECTORIZE_SSE3
        //   Packet4f tmp = _mm_add_ps(a, vec4f_swizzle1(a,2,3,2,3));
        //   return pfirst<Packet4f>(_mm_hadd_ps(tmp, tmp));
        // #else
        Packet4f tmp = _mm_add_ps(a, _mm_movehl_ps(a, a));
        return pfirst<Packet4f>(_mm_add_ss(tmp, _mm_shuffle_ps(tmp, tmp, 1)));
        // #endif
    }

    template <> EIGEN_STRONG_INLINE double predux<Packet2d>(const Packet2d& a)
    {
        // Disable SSE3 _mm_hadd_pd that is extremely slow on all existing Intel's architectures
        // (from Nehalem to Haswell)
        // #ifdef EIGEN_VECTORIZE_SSE3
        //   return pfirst<Packet2d>(_mm_hadd_pd(a, a));
        // #else
        return pfirst<Packet2d>(_mm_add_sd(a, _mm_unpackhi_pd(a, a)));
        // #endif
    }

#ifdef EIGEN_VECTORIZE_SSSE3
    template <> EIGEN_STRONG_INLINE int predux<Packet4i>(const Packet4i& a)
    {
        Packet4i tmp0 = _mm_hadd_epi32(a, a);
        return pfirst<Packet4i>(_mm_hadd_epi32(tmp0, tmp0));
    }

#else
    template <> EIGEN_STRONG_INLINE int predux<Packet4i>(const Packet4i& a)
    {
        Packet4i tmp = _mm_add_epi32(a, _mm_unpackhi_epi64(a, a));
        return pfirst(tmp) + pfirst<Packet4i>(_mm_shuffle_epi32(tmp, 1));
    }
#endif

    template <> EIGEN_STRONG_INLINE bool predux<Packet16b>(const Packet16b& a)
    {
        Packet4i tmp = _mm_or_si128(a, _mm_unpackhi_epi64(a, a));
        return (pfirst(tmp) != 0) || (pfirst<Packet4i>(_mm_shuffle_epi32(tmp, 1)) != 0);
    }

    // Other reduction functions:

    // mul
    template <> EIGEN_STRONG_INLINE float predux_mul<Packet4f>(const Packet4f& a)
    {
        Packet4f tmp = _mm_mul_ps(a, _mm_movehl_ps(a, a));
        return pfirst<Packet4f>(_mm_mul_ss(tmp, _mm_shuffle_ps(tmp, tmp, 1)));
    }
    template <> EIGEN_STRONG_INLINE double predux_mul<Packet2d>(const Packet2d& a) { return pfirst<Packet2d>(_mm_mul_sd(a, _mm_unpackhi_pd(a, a))); }
    template <> EIGEN_STRONG_INLINE int predux_mul<Packet4i>(const Packet4i& a)
    {
        // after some experiments, it is seems this is the fastest way to implement it
        // for GCC (eg., reusing pmul is very slow !)
        // TODO try to call _mm_mul_epu32 directly
        EIGEN_ALIGN16 int aux[4];
        pstore(aux, a);
        return (aux[0] * aux[1]) * (aux[2] * aux[3]);
    }

    template <> EIGEN_STRONG_INLINE bool predux_mul<Packet16b>(const Packet16b& a)
    {
        Packet4i tmp = _mm_and_si128(a, _mm_unpackhi_epi64(a, a));
        return ((pfirst<Packet4i>(tmp) == 0x01010101) && (pfirst<Packet4i>(_mm_shuffle_epi32(tmp, 1)) == 0x01010101));
    }

    // min
    template <> EIGEN_STRONG_INLINE float predux_min<Packet4f>(const Packet4f& a)
    {
        Packet4f tmp = _mm_min_ps(a, _mm_movehl_ps(a, a));
        return pfirst<Packet4f>(_mm_min_ss(tmp, _mm_shuffle_ps(tmp, tmp, 1)));
    }
    template <> EIGEN_STRONG_INLINE double predux_min<Packet2d>(const Packet2d& a) { return pfirst<Packet2d>(_mm_min_sd(a, _mm_unpackhi_pd(a, a))); }
    template <> EIGEN_STRONG_INLINE int predux_min<Packet4i>(const Packet4i& a)
    {
#ifdef EIGEN_VECTORIZE_SSE4_1
        Packet4i tmp = _mm_min_epi32(a, _mm_shuffle_epi32(a, _MM_SHUFFLE(0, 0, 3, 2)));
        return pfirst<Packet4i>(_mm_min_epi32(tmp, _mm_shuffle_epi32(tmp, 1)));
#else
        // after some experiments, it is seems this is the fastest way to implement it
        // for GCC (eg., it does not like using std::min after the pstore !!)
        EIGEN_ALIGN16 int aux[4];
        pstore(aux, a);
        int aux0 = aux[0] < aux[1] ? aux[0] : aux[1];
        int aux2 = aux[2] < aux[3] ? aux[2] : aux[3];
        return aux0 < aux2 ? aux0 : aux2;
#endif  // EIGEN_VECTORIZE_SSE4_1
    }

    // max
    template <> EIGEN_STRONG_INLINE float predux_max<Packet4f>(const Packet4f& a)
    {
        Packet4f tmp = _mm_max_ps(a, _mm_movehl_ps(a, a));
        return pfirst<Packet4f>(_mm_max_ss(tmp, _mm_shuffle_ps(tmp, tmp, 1)));
    }
    template <> EIGEN_STRONG_INLINE double predux_max<Packet2d>(const Packet2d& a) { return pfirst<Packet2d>(_mm_max_sd(a, _mm_unpackhi_pd(a, a))); }
    template <> EIGEN_STRONG_INLINE int predux_max<Packet4i>(const Packet4i& a)
    {
#ifdef EIGEN_VECTORIZE_SSE4_1
        Packet4i tmp = _mm_max_epi32(a, _mm_shuffle_epi32(a, _MM_SHUFFLE(0, 0, 3, 2)));
        return pfirst<Packet4i>(_mm_max_epi32(tmp, _mm_shuffle_epi32(tmp, 1)));
#else
        // after some experiments, it is seems this is the fastest way to implement it
        // for GCC (eg., it does not like using std::min after the pstore !!)
        EIGEN_ALIGN16 int aux[4];
        pstore(aux, a);
        int aux0 = aux[0] > aux[1] ? aux[0] : aux[1];
        int aux2 = aux[2] > aux[3] ? aux[2] : aux[3];
        return aux0 > aux2 ? aux0 : aux2;
#endif  // EIGEN_VECTORIZE_SSE4_1
    }

    // not needed yet
    // template<> EIGEN_STRONG_INLINE bool predux_all(const Packet4f& x)
    // {
    //   return _mm_movemask_ps(x) == 0xF;
    // }

    template <> EIGEN_STRONG_INLINE bool predux_any(const Packet4f& x) { return _mm_movemask_ps(x) != 0x0; }

    EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet4f, 4>& kernel)
    {
        _MM_TRANSPOSE4_PS(kernel.packet[0], kernel.packet[1], kernel.packet[2], kernel.packet[3]);
    }

    EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet2d, 2>& kernel)
    {
        __m128d tmp = _mm_unpackhi_pd(kernel.packet[0], kernel.packet[1]);
        kernel.packet[0] = _mm_unpacklo_pd(kernel.packet[0], kernel.packet[1]);
        kernel.packet[1] = tmp;
    }

    EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet4i, 4>& kernel)
    {
        __m128i T0 = _mm_unpacklo_epi32(kernel.packet[0], kernel.packet[1]);
        __m128i T1 = _mm_unpacklo_epi32(kernel.packet[2], kernel.packet[3]);
        __m128i T2 = _mm_unpackhi_epi32(kernel.packet[0], kernel.packet[1]);
        __m128i T3 = _mm_unpackhi_epi32(kernel.packet[2], kernel.packet[3]);

        kernel.packet[0] = _mm_unpacklo_epi64(T0, T1);
        kernel.packet[1] = _mm_unpackhi_epi64(T0, T1);
        kernel.packet[2] = _mm_unpacklo_epi64(T2, T3);
        kernel.packet[3] = _mm_unpackhi_epi64(T2, T3);
    }

    EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet16b, 4>& kernel)
    {
        __m128i T0 = _mm_unpacklo_epi8(kernel.packet[0], kernel.packet[1]);
        __m128i T1 = _mm_unpackhi_epi8(kernel.packet[0], kernel.packet[1]);
        __m128i T2 = _mm_unpacklo_epi8(kernel.packet[2], kernel.packet[3]);
        __m128i T3 = _mm_unpackhi_epi8(kernel.packet[2], kernel.packet[3]);
        kernel.packet[0] = _mm_unpacklo_epi16(T0, T2);
        kernel.packet[1] = _mm_unpackhi_epi16(T0, T2);
        kernel.packet[2] = _mm_unpacklo_epi16(T1, T3);
        kernel.packet[3] = _mm_unpackhi_epi16(T1, T3);
    }

    EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet16b, 16>& kernel)
    {
        // If we number the elements in the input thus:
        // kernel.packet[ 0] = {00, 01, 02, 03, 04, 05, 06, 07, 08, 09, 0a, 0b, 0c, 0d, 0e, 0f}
        // kernel.packet[ 1] = {10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1a, 1b, 1c, 1d, 1e, 1f}
        // ...
        // kernel.packet[15] = {f0, f1, f2, f3, f4, f5, f6, f7, f8, f9, fa, fb, fc, fd, fe, ff},
        //
        // the desired output is:
        // kernel.packet[ 0] = {00, 10, 20, 30, 40, 50, 60, 70, 80, 90, a0, b0, c0, d0, e0, f0}
        // kernel.packet[ 1] = {01, 11, 21, 31, 41, 51, 61, 71, 81, 91, a1, b1, c1, d1, e1, f1}
        // ...
        // kernel.packet[15] = {0f, 1f, 2f, 3f, 4f, 5f, 6f, 7f, 8f, 9f, af, bf, cf, df, ef, ff},
        __m128i t0 = _mm_unpacklo_epi8(kernel.packet[0], kernel.packet[1]);  // 00 10 01 11 02 12 03 13 04 14 05 15 06 16 07 17
        __m128i t1 = _mm_unpackhi_epi8(kernel.packet[0], kernel.packet[1]);  // 08 18 09 19 0a 1a 0b 1b 0c 1c 0d 1d 0e 1e 0f 1f
        __m128i t2 = _mm_unpacklo_epi8(kernel.packet[2], kernel.packet[3]);  // 20 30 21 31 22 32 ...                     27 37
        __m128i t3 = _mm_unpackhi_epi8(kernel.packet[2], kernel.packet[3]);  // 28 38 29 39 2a 3a ...                     2f 3f
        __m128i t4 = _mm_unpacklo_epi8(kernel.packet[4], kernel.packet[5]);  // 40 50 41 51 42 52                         47 57
        __m128i t5 = _mm_unpackhi_epi8(kernel.packet[4], kernel.packet[5]);  // 48 58 49 59 4a 5a
        __m128i t6 = _mm_unpacklo_epi8(kernel.packet[6], kernel.packet[7]);
        __m128i t7 = _mm_unpackhi_epi8(kernel.packet[6], kernel.packet[7]);
        __m128i t8 = _mm_unpacklo_epi8(kernel.packet[8], kernel.packet[9]);
        __m128i t9 = _mm_unpackhi_epi8(kernel.packet[8], kernel.packet[9]);
        __m128i ta = _mm_unpacklo_epi8(kernel.packet[10], kernel.packet[11]);
        __m128i tb = _mm_unpackhi_epi8(kernel.packet[10], kernel.packet[11]);
        __m128i tc = _mm_unpacklo_epi8(kernel.packet[12], kernel.packet[13]);
        __m128i td = _mm_unpackhi_epi8(kernel.packet[12], kernel.packet[13]);
        __m128i te = _mm_unpacklo_epi8(kernel.packet[14], kernel.packet[15]);
        __m128i tf = _mm_unpackhi_epi8(kernel.packet[14], kernel.packet[15]);

        __m128i s0 = _mm_unpacklo_epi16(t0, t2);  // 00 10 20 30 01 11 21 31 02 12 22 32 03 13 23 33
        __m128i s1 = _mm_unpackhi_epi16(t0, t2);  // 04 14 24 34
        __m128i s2 = _mm_unpacklo_epi16(t1, t3);  // 08 18 28 38 ...
        __m128i s3 = _mm_unpackhi_epi16(t1, t3);  // 0c 1c 2c 3c ...
        __m128i s4 = _mm_unpacklo_epi16(t4, t6);  // 40 50 60 70 41 51 61 71 42 52 62 72 43 53 63 73
        __m128i s5 = _mm_unpackhi_epi16(t4, t6);  // 44 54 64 74 ...
        __m128i s6 = _mm_unpacklo_epi16(t5, t7);
        __m128i s7 = _mm_unpackhi_epi16(t5, t7);
        __m128i s8 = _mm_unpacklo_epi16(t8, ta);
        __m128i s9 = _mm_unpackhi_epi16(t8, ta);
        __m128i sa = _mm_unpacklo_epi16(t9, tb);
        __m128i sb = _mm_unpackhi_epi16(t9, tb);
        __m128i sc = _mm_unpacklo_epi16(tc, te);
        __m128i sd = _mm_unpackhi_epi16(tc, te);
        __m128i se = _mm_unpacklo_epi16(td, tf);
        __m128i sf = _mm_unpackhi_epi16(td, tf);

        __m128i u0 = _mm_unpacklo_epi32(s0, s4);  // 00 10 20 30 40 50 60 70 01 11 21 31 41 51 61 71
        __m128i u1 = _mm_unpackhi_epi32(s0, s4);  // 02 12 22 32 42 52 62 72 03 13 23 33 43 53 63 73
        __m128i u2 = _mm_unpacklo_epi32(s1, s5);
        __m128i u3 = _mm_unpackhi_epi32(s1, s5);
        __m128i u4 = _mm_unpacklo_epi32(s2, s6);
        __m128i u5 = _mm_unpackhi_epi32(s2, s6);
        __m128i u6 = _mm_unpacklo_epi32(s3, s7);
        __m128i u7 = _mm_unpackhi_epi32(s3, s7);
        __m128i u8 = _mm_unpacklo_epi32(s8, sc);
        __m128i u9 = _mm_unpackhi_epi32(s8, sc);
        __m128i ua = _mm_unpacklo_epi32(s9, sd);
        __m128i ub = _mm_unpackhi_epi32(s9, sd);
        __m128i uc = _mm_unpacklo_epi32(sa, se);
        __m128i ud = _mm_unpackhi_epi32(sa, se);
        __m128i ue = _mm_unpacklo_epi32(sb, sf);
        __m128i uf = _mm_unpackhi_epi32(sb, sf);

        kernel.packet[0] = _mm_unpacklo_epi64(u0, u8);
        kernel.packet[1] = _mm_unpackhi_epi64(u0, u8);
        kernel.packet[2] = _mm_unpacklo_epi64(u1, u9);
        kernel.packet[3] = _mm_unpackhi_epi64(u1, u9);
        kernel.packet[4] = _mm_unpacklo_epi64(u2, ua);
        kernel.packet[5] = _mm_unpackhi_epi64(u2, ua);
        kernel.packet[6] = _mm_unpacklo_epi64(u3, ub);
        kernel.packet[7] = _mm_unpackhi_epi64(u3, ub);
        kernel.packet[8] = _mm_unpacklo_epi64(u4, uc);
        kernel.packet[9] = _mm_unpackhi_epi64(u4, uc);
        kernel.packet[10] = _mm_unpacklo_epi64(u5, ud);
        kernel.packet[11] = _mm_unpackhi_epi64(u5, ud);
        kernel.packet[12] = _mm_unpacklo_epi64(u6, ue);
        kernel.packet[13] = _mm_unpackhi_epi64(u6, ue);
        kernel.packet[14] = _mm_unpacklo_epi64(u7, uf);
        kernel.packet[15] = _mm_unpackhi_epi64(u7, uf);
    }

    template <> EIGEN_STRONG_INLINE Packet4i pblend(const Selector<4>& ifPacket, const Packet4i& thenPacket, const Packet4i& elsePacket)
    {
        const __m128i zero = _mm_setzero_si128();
        const __m128i select = _mm_set_epi32(ifPacket.select[3], ifPacket.select[2], ifPacket.select[1], ifPacket.select[0]);
        __m128i false_mask = _mm_cmpeq_epi32(select, zero);
#ifdef EIGEN_VECTORIZE_SSE4_1
        return _mm_blendv_epi8(thenPacket, elsePacket, false_mask);
#else
        return _mm_or_si128(_mm_andnot_si128(false_mask, thenPacket), _mm_and_si128(false_mask, elsePacket));
#endif
    }
    template <> EIGEN_STRONG_INLINE Packet4f pblend(const Selector<4>& ifPacket, const Packet4f& thenPacket, const Packet4f& elsePacket)
    {
        const __m128 zero = _mm_setzero_ps();
        const __m128 select = _mm_set_ps(ifPacket.select[3], ifPacket.select[2], ifPacket.select[1], ifPacket.select[0]);
        __m128 false_mask = _mm_cmpeq_ps(select, zero);
#ifdef EIGEN_VECTORIZE_SSE4_1
        return _mm_blendv_ps(thenPacket, elsePacket, false_mask);
#else
        return _mm_or_ps(_mm_andnot_ps(false_mask, thenPacket), _mm_and_ps(false_mask, elsePacket));
#endif
    }
    template <> EIGEN_STRONG_INLINE Packet2d pblend(const Selector<2>& ifPacket, const Packet2d& thenPacket, const Packet2d& elsePacket)
    {
        const __m128d zero = _mm_setzero_pd();
        const __m128d select = _mm_set_pd(ifPacket.select[1], ifPacket.select[0]);
        __m128d false_mask = _mm_cmpeq_pd(select, zero);
#ifdef EIGEN_VECTORIZE_SSE4_1
        return _mm_blendv_pd(thenPacket, elsePacket, false_mask);
#else
        return _mm_or_pd(_mm_andnot_pd(false_mask, thenPacket), _mm_and_pd(false_mask, elsePacket));
#endif
    }

// Scalar path for pmadd with FMA to ensure consistency with vectorized path.
#ifdef EIGEN_VECTORIZE_FMA
    template <> EIGEN_STRONG_INLINE float pmadd(const float& a, const float& b, const float& c) { return ::fmaf(a, b, c); }
    template <> EIGEN_STRONG_INLINE double pmadd(const double& a, const double& b, const double& c) { return ::fma(a, b, c); }
#endif

// Packet math for Eigen::half
// Disable the following code since it's broken on too many platforms / compilers.
//#elif defined(EIGEN_VECTORIZE_SSE) && (!EIGEN_ARCH_x86_64) && (!EIGEN_COMP_MSVC)
#if 0

typedef struct {
  __m64 x;
} Packet4h;


template<> struct is_arithmetic<Packet4h> { enum { value = true }; };

template <>
struct packet_traits<Eigen::half> : default_packet_traits {
  typedef Packet4h type;
  // There is no half-size packet for Packet4h.
  typedef Packet4h half;
  enum {
    Vectorizable = 1,
    AlignedOnScalar = 1,
    size = 4,
    HasHalfPacket = 0,
    HasAdd    = 1,
    HasSub    = 1,
    HasMul    = 1,
    HasDiv    = 1,
    HasNegate = 0,
    HasAbs    = 0,
    HasAbs2   = 0,
    HasMin    = 0,
    HasMax    = 0,
    HasConj   = 0,
    HasSetLinear = 0,
    HasSqrt = 0,
    HasRsqrt = 0,
    HasExp = 0,
    HasLog = 0,
    HasBlend = 0
  };
};


template<> struct unpacket_traits<Packet4h> { typedef Eigen::half type; enum {size=4, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef Packet4h half; };

template<> EIGEN_STRONG_INLINE Packet4h pset1<Packet4h>(const Eigen::half& from) {
  Packet4h result;
  result.x = _mm_set1_pi16(from.x);
  return result;
}

template<> EIGEN_STRONG_INLINE Eigen::half pfirst<Packet4h>(const Packet4h& from) {
  return half_impl::raw_uint16_to_half(static_cast<unsigned short>(_mm_cvtsi64_si32(from.x)));
}

template<> EIGEN_STRONG_INLINE Packet4h pconj(const Packet4h& a) { return a; }

template<> EIGEN_STRONG_INLINE Packet4h padd<Packet4h>(const Packet4h& a, const Packet4h& b) {
  __int64_t a64 = _mm_cvtm64_si64(a.x);
  __int64_t b64 = _mm_cvtm64_si64(b.x);

  Eigen::half h[4];

  Eigen::half ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64));
  Eigen::half hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64));
  h[0] = ha + hb;
  ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 16));
  hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 16));
  h[1] = ha + hb;
  ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 32));
  hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 32));
  h[2] = ha + hb;
  ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 48));
  hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 48));
  h[3] = ha + hb;
  Packet4h result;
  result.x = _mm_set_pi16(h[3].x, h[2].x, h[1].x, h[0].x);
  return result;
}

template<> EIGEN_STRONG_INLINE Packet4h psub<Packet4h>(const Packet4h& a, const Packet4h& b) {
  __int64_t a64 = _mm_cvtm64_si64(a.x);
  __int64_t b64 = _mm_cvtm64_si64(b.x);

  Eigen::half h[4];

  Eigen::half ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64));
  Eigen::half hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64));
  h[0] = ha - hb;
  ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 16));
  hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 16));
  h[1] = ha - hb;
  ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 32));
  hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 32));
  h[2] = ha - hb;
  ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 48));
  hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 48));
  h[3] = ha - hb;
  Packet4h result;
  result.x = _mm_set_pi16(h[3].x, h[2].x, h[1].x, h[0].x);
  return result;
}

template<> EIGEN_STRONG_INLINE Packet4h pmul<Packet4h>(const Packet4h& a, const Packet4h& b) {
  __int64_t a64 = _mm_cvtm64_si64(a.x);
  __int64_t b64 = _mm_cvtm64_si64(b.x);

  Eigen::half h[4];

  Eigen::half ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64));
  Eigen::half hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64));
  h[0] = ha * hb;
  ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 16));
  hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 16));
  h[1] = ha * hb;
  ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 32));
  hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 32));
  h[2] = ha * hb;
  ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 48));
  hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 48));
  h[3] = ha * hb;
  Packet4h result;
  result.x = _mm_set_pi16(h[3].x, h[2].x, h[1].x, h[0].x);
  return result;
}

template<> EIGEN_STRONG_INLINE Packet4h pdiv<Packet4h>(const Packet4h& a, const Packet4h& b) {
  __int64_t a64 = _mm_cvtm64_si64(a.x);
  __int64_t b64 = _mm_cvtm64_si64(b.x);

  Eigen::half h[4];

  Eigen::half ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64));
  Eigen::half hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64));
  h[0] = ha / hb;
  ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 16));
  hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 16));
  h[1] = ha / hb;
  ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 32));
  hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 32));
  h[2] = ha / hb;
  ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 48));
  hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 48));
  h[3] = ha / hb;
  Packet4h result;
  result.x = _mm_set_pi16(h[3].x, h[2].x, h[1].x, h[0].x);
  return result;
}

template<> EIGEN_STRONG_INLINE Packet4h pload<Packet4h>(const Eigen::half* from) {
  Packet4h result;
  result.x = _mm_cvtsi64_m64(*reinterpret_cast<const __int64_t*>(from));
  return result;
}

template<> EIGEN_STRONG_INLINE Packet4h ploadu<Packet4h>(const Eigen::half* from) {
  Packet4h result;
  result.x = _mm_cvtsi64_m64(*reinterpret_cast<const __int64_t*>(from));
  return result;
}

template<> EIGEN_STRONG_INLINE void pstore<Eigen::half>(Eigen::half* to, const Packet4h& from) {
  __int64_t r = _mm_cvtm64_si64(from.x);
  *(reinterpret_cast<__int64_t*>(to)) = r;
}

template<> EIGEN_STRONG_INLINE void pstoreu<Eigen::half>(Eigen::half* to, const Packet4h& from) {
  __int64_t r = _mm_cvtm64_si64(from.x);
  *(reinterpret_cast<__int64_t*>(to)) = r;
}

template<> EIGEN_STRONG_INLINE Packet4h
ploadquad<Packet4h>(const Eigen::half* from) {
  return pset1<Packet4h>(*from);
}

template<> EIGEN_STRONG_INLINE Packet4h pgather<Eigen::half, Packet4h>(const Eigen::half* from, Index stride)
{
  Packet4h result;
  result.x = _mm_set_pi16(from[3*stride].x, from[2*stride].x, from[1*stride].x, from[0*stride].x);
  return result;
}

template<> EIGEN_STRONG_INLINE void pscatter<Eigen::half, Packet4h>(Eigen::half* to, const Packet4h& from, Index stride)
{
  __int64_t a = _mm_cvtm64_si64(from.x);
  to[stride*0].x = static_cast<unsigned short>(a);
  to[stride*1].x = static_cast<unsigned short>(a >> 16);
  to[stride*2].x = static_cast<unsigned short>(a >> 32);
  to[stride*3].x = static_cast<unsigned short>(a >> 48);
}

EIGEN_STRONG_INLINE void
ptranspose(PacketBlock<Packet4h,4>& kernel) {
  __m64 T0 = _mm_unpacklo_pi16(kernel.packet[0].x, kernel.packet[1].x);
  __m64 T1 = _mm_unpacklo_pi16(kernel.packet[2].x, kernel.packet[3].x);
  __m64 T2 = _mm_unpackhi_pi16(kernel.packet[0].x, kernel.packet[1].x);
  __m64 T3 = _mm_unpackhi_pi16(kernel.packet[2].x, kernel.packet[3].x);

  kernel.packet[0].x = _mm_unpacklo_pi32(T0, T1);
  kernel.packet[1].x = _mm_unpackhi_pi32(T0, T1);
  kernel.packet[2].x = _mm_unpacklo_pi32(T2, T3);
  kernel.packet[3].x = _mm_unpackhi_pi32(T2, T3);
}

#endif

}  // end namespace internal

}  // end namespace Eigen

#if EIGEN_COMP_PGI && EIGEN_COMP_PGI < 1900
// PGI++ does not define the following intrinsics in C++ mode.
static inline __m128 _mm_castpd_ps(__m128d x) { return reinterpret_cast<__m128&>(x); }
static inline __m128i _mm_castpd_si128(__m128d x) { return reinterpret_cast<__m128i&>(x); }
static inline __m128d _mm_castps_pd(__m128 x) { return reinterpret_cast<__m128d&>(x); }
static inline __m128i _mm_castps_si128(__m128 x) { return reinterpret_cast<__m128i&>(x); }
static inline __m128 _mm_castsi128_ps(__m128i x) { return reinterpret_cast<__m128&>(x); }
static inline __m128d _mm_castsi128_pd(__m128i x) { return reinterpret_cast<__m128d&>(x); }
#endif

#endif  // EIGEN_PACKET_MATH_SSE_H
